数学专业英语(Doc版).9

学专业英语－How to Organize a paper (For Beginers)?

The usual journal article is aimed at experts and near-experts, who are the peo ple most likely to read it. Your purpose should be say quickly what you have done is good, and why it works. Avoid lengthy summaries of known results, and minimize the preliminaries to the statements of your main results. There ar e many good ways of organizing a paper which can be learned by studying pa pers of the better expositors. The following suggestions describe a standard acc eptable style.

Choose a title which helps the reader place in the body of mathematics. A use less title: Concerning some applications of a theorem of J. Doe. A. good title contains several well-known key words, e. g. Algebraic solutions of linear parti al differential equations. Make the title as informative as possible; but avoid re dundancy, and eschew the medieval practice of letting the title serve as an infl ated advertisement. A title of more than ten or twelve words is likely to be m iscopied, misquoted, distorted, and cursed.

The first paragraph of the introduction should be comprehensible to any mathe matician, and it should pinpoint the location of the subject matter. The main p urpose of the introduction is to present a rough statement of the principal resul ts; include this statement as soon as it is feasible to do so, although it is som etimes well to set the stage with a preliminary paragraph. The remainder of th e introduction can discuss the connections with other results.

It is sometimes useful to follow the introduction with a brief section that estab lishes notation and refers to standard sources for basic concepts and results. N ormally this section should be less than a page in length. Some authors weave this information unobtrusively into their introductions, avoiding thereby a dull section.

The section following the introduction should contain the statement of one or more principal results. The rule that the statement of a theorem should precede its proof a triviality. A reader wants to know the objective of the paper, as well as the relevance of each section, as it is being read. In the case of a ma jor theorem whose proof is long, its statement can be followed by an outline of proof with references to subsequent sections for proofs of the various parts. Strive for proofs that are conceptual rather than computational. For an example of the difference, see A Mathematician’s Miscellany by J.E.Littlewood, in wh ich the contrast between barbaric and civilized proofs is beautifully and amusin gly portrayed. To achieve conceptual proofs, it is often helpful for an author t o adopt an initial attitude such as one would take when communicating mathe matics orally (as when walking with a friend). Decide how to state results wit h a minimum of symbols and how to express the ideas of the proof without c

omputations. Then add to this framework the details needed to clinch the resul ts.

Omit any computation which is routine (i.e. does not depend on unexpected tri cks). Merely indicate the starting point, describe the procedure, and state the o utcome.

It is good research practice to analyze an argument by breaking it into a succe ssion of lemmas, each stated with maximum generality. It is usually bad practi ce to try to publish such an analysis, since it is likely to be long and unintere sting. The reader wants to see the path-not examine it with a microscope. A p art of the argument is worth isolating as a lemma if it is used at least twice l ater on.

The rudiments of grammar are important. The few lines written on the blackbo ard during an hour’s lecture are augmented by spoken commentary, and aat t he end of the day they are washed away by a merciful janitor. Since the publ ished paper will forever speak for its author without benefit of the cleansing s ponge, careful attention to sentence structure is worthwhile. Each author must develop a suitable individual style; a few general suggestions are nevertheless a ppropriate.

The barbarism called the dangling participle has recently become more prevalen t, but not less loathsome. “Differentiating both sides with respect to x, the eq uation becomes---”is wrong, because “the equation”cannot be the subject th at does the differentiation. Write instead “differentiating both sides with respec t to x, we get the equation---,”or “Differentiation of both sides with respect to x leads to the equation---”

Although the notion has gained some currency, it is absurd to claim that infor mal “we”has no proper place in mathematical exposition. Strict formality is appropriate in the statement of a theorem, and casual chatting should indeed b e banished from those parts of a paper which will be printed in italics. But fif teen consecutive pages of formality are altogether foreign to the spirit of the t wentieth century, and nearly all authors who try to sustain an impersonal digni fied text of such length succeed merely in erecting elaborate monuments to slu msiness.

A sentence of the form “if P,Q”can be understood. However “if P,Q,R,S,T”is not so good, even if it can be deduced from the context that the third co mma is the one that serves the role of “then.”The reader is looking at the paper to learn something, not with a desire for mental calisthenics.

Vocabulary

preliminary 序,小引(名)开端的,最初的(形) eschew 避

免

medieval 中古的，中世纪的

inflated 夸张的

comprehensible 可领悟的，可了解的pinpoint 准确指出（位置）

weave 插入，嵌入

unobtrusivcly 无妨碍地

triviality 平凡琐事

barbarism 野蛮，未开化

portray 写真，描写

clinch 使终结

rudiment 初步，基础

commentary 注解，说明

janitor 看守房屋者

sponge 海绵

dangling participle 不连结分词prevalent 流行的，盛行

loathsome 可恶地

absurd 荒谬的

banish 排除

sustain 维持，继续

slumsiness 粗俗，笨拙

monument 纪念碑

calisthenics 柔软体操，健美体操

notes

1. 本课文选自美国数学会出版的小册子A mamual for authors of mathematical paper的一节，本文对准备投寄英文稿件的读者值得一读。

2. Choose a title which helps the reader place in the body of mathematics.

意思是：选择一个可帮助读者进入数学核心的标题。

3．For an example of the difference, ……in which the contrast between barbaric and civilized proofs is beautifully and amusingly portrayed.

意思是：作为这种差别的一个例子，可参看J.E.Littlewood A mathematician’s Miscellany一文，在那里，他把野蛮的（令人讨厌的）证明与文明的证明这两者之间的对比很漂亮地和有趣地给予描绘出来，这里“差别”是指conceptual proof 与computation proof 差别。Portray的意思是：“人像”，这里作动词用，作“描绘”解。

4．The reader wants to see the path--------not to examine it with a microscope.

意思是：读者想知道的是有关论证的途径——而不想使用显微镜去观察。这里作者所要表达的意思是：写文章的人只需把论证的要点写出即可，无需把论证的整个分析过程写得过于冗长。

5．The barbarism called the dangling participles had recently become prevalent, but not less loathsome.

意思是：一种称为“不连结分词”的句子，最近变得盛行起来，但这类句子毕竟是令人讨厌的。关于“不连结分词”，请参看ⅡA第三课注2。

6．The reader is looking at the paper to learn something, not with a desire for mental calisthenics.

意思是：读者阅读文章是为了学到一点东西，而不是抱着一种做智力体操的愿望去阅读的。这里作者是在批评有些写文章的人使用了一些令读者摸不着头脑，而要读者去猜其真实意思的句子（例如用”if P, Q,R,S,T”表达”if P,Q,R then S,T这样的句子。）

Exercise

(Miscellaneous exercises (continued))

Ⅰ.Translate the following sentensces into English:

1. 若行列式中有两行成比例，则行列式为零。

2. 矩阵和矩阵是两种常用的矩阵

3. 两个次多项式上的值相等，则

4. 对任意两个多项式一定存在有多项式或者相等于零或者它的次数小于的次数。

5. 如果取双曲线的渐近线做为坐标轴，则双曲线方程将得到特别简单的形式。

6. 抛物线与椭圆和双曲线不同，它没有中心，它的另一个特殊性是它仅有一个焦点。

7. 通过平面上任何5个不同的点，其中没有4点同在一直线上（共线），有一条仅有一条二级曲线。

8. 当椭圆的长轴等于它的短轴时，它化为一圆。

9. 显然，无界序列不收敛。

10. 设在[a,b]上连续，若存在两个点，则必有

11. 若我们能证明连续函数级数在紧集D上一致收敛，则在此集上可对级数进行逐项积分。

12. 此定理给出了用n次泰勒多项式来近似代替时余项太小的一种估计。

13. 用同样的方法，我们还可以证明定理A。

14. 定理中的条件是缺一不可的。

15. 最后，我们再举出两个能说明问题的例子来结束文章。

Ⅱ.Translate the following sentences into Chinese(Pay attention to the words underlined):

1. The compact and Fredholm operators lately have been receiving renewed attention because of the a pplications to integral operators and partial differential elliptic operators.

2. We dcnote by [x] the greatest integral part which is less than or equal to x.

3. Global analysis on manifolds has come into its owm, both in its integral and differential aspects. It is therefore desirable to integrate manifolds in analysis courses.

Ⅲ.Translate the following passages into Chinese:

1. The concept of ordering was abstracted form various relations, such as the inequality relation betw een real numbers and the inclusion relation between sets. Suppose that we are given a set X={x, y, z ,…}，the relation between the elements of X, denoted by

2. Suppose we are given a relation R (usually denoted by the symbol ) between elements of a set X such that for any elements x and y of X, either xRy orits negation holds The relation is called an equi valence relation (on X)if it satisfies the following three conditions:

(i) xRx

(ii) xRy implies yRx,

(iii) xRy and yRz imply xRz.

Conditions (i),(ii),and(iii)are called the reflexive, symmetric and transitive laws respectively. Together they are called equivalence properties. The relations of congruence and similarity between figures are equivale nce relations.